The equation representing the given case is 2(x - 8) = 3(x + 3), where x is the number.
The number satisfying this equation is -25.
In the question, we are asked to find the number when twice the difference of the number and 8 is equal to thrice the sum of the number and 3.
We assume the number to be x.
The expression representing twice the difference between the number and 8, can be shown as 2(x - 8).
The expression representing thrice the sum of the number and 3, can be shown as 3(x + 3).
We are informed that these two expressions are equal. This can be shown as the equation:
2(x - 8) = 3(x + 3).
Thus, the equation representing the given case is 2(x - 8) = 3(x + 3), where x is the number.
Now, to find the number, we solve the equation as follows:
2(x - 8) = 3(x + 3),
or, 2x - 16 = 3x + 9 {Simplifying},
or, 2x - 16 + (16 - 3x) = 3x + 9 + (16 - 3x) {Adding (16 - 3x) to both sides of the equation},
or, 2x - 16 + 16 - 3x = 3x + 9 + 16 - 3x {Simplifying},
or, -x = 25 {Simplifying},
or, -x(-1) = 25(-1) {Multiplying both sides of the equation with -1},
or, x = -25 {Simplifying}.
Thus, the number satisfying the equation is -25.
Learn more about solving equations at
https://brainly.com/question/1691934
#SPJ4
